152 Utilisation and conservation of farm animal genetic resources
John Woolliams
management problem. However for a ixed mating population of M breeding males and dM breeding females generation an achievable lower bound has been established.
his was described by Sanchez et al. 2003 ater considering the minimisation of long-
term contributions. Firstly consider only random mating α ≈ 0. he study showed that: minimum ΔF ≥ [1+2¼
d
][12M] ~ 1[12M] for large d, and importantly showed how this could be achieved. his is shown in Figure 2. he principles extend
the initial observations of Gowe et al. 1959 that a sire should be replaced by a son and
a daughter by a dam; and those of Wang 1997, who recognised that for d 1 there was an imbalance whereby a dam of a selected son is favoured and should not therefore
contribute a daughter, instead a diferent dam should contribute 2 daughters to more equally distribute the contributions. he extension of Sanchez
et al. 2003 recognises that minimising ΔF requires management across generations and so the breeding
purpose of each dam is determined from its own dam’s breeding purpose, as in Figure 7.2. he distinction is that selecting without reference to previous generations allows equal
initial contributions to develop into unequal long-term contributions. For example the CV of long-term contributions for the system of Wang 1997 among breeding males is
~ 1[2√2] = 0.35 for large
d compared to 0 for Sanchez et al. 2003. hese comparisons are made
without managing mating. Wang 1997 shows that by introducing the avoidance of relatives in mating α 0, ΔF can be made close to the
value obtained by Sanchez et al. 2003 for random mating. his is efective for Wang
1997 since as a general rule α 0 reduces the variation of contributions about the desired expectations across generations. However Sanchez
et al. 2003 showed that, by introducing a degree of preferential mating of relatives, consistent with the general
Inherited labels Males 1
‘1’ has all Females 2, 3 4
‘2’ has a ‘1’ ‘3’ has a ‘2’
‘4’ has a ‘3’ ‘4’
1 1
1 2
2 2
2 3
3 3
3 4
4 4
4
t+1 t
t-1
1
Figure 7.2. he design that achieves the lower bound for ΔF with random mating for d=3. Fiteen diferent individuals are shown, labelled within generations. Following Sanchez et al.
2003.
Utilisation and conservation of farm animal genetic resources 153
Chapter 7. Genetic contributions and inbreeding
principles outlined at the start of this section, ΔF could be reduced further below the bound for random mating. It may be questioned whether or not the preferential mating
of relatives is desirable in practice: on the positive side, 1 any degree of preferential mating is beneicial and need not be great, and 2 it is consistent with ideas of purging;
on the negative side 3 there may be a greater inbreeding depression for some individuals depending on the degree of preference. Resolving such an issue will depend on the
recent breeding history of the population and its potential genetic load.
3.2. Implementation
What should be done in practice? he challenges caused by implementation are exempliied by a dam that is intended to produce a son instead only having daughters
or vice versa not such a problem with many ish species where sex is more labile. his
requires the highly designed schemes to be robust. At present, robustness of mating schemes is still an area of debate and further work is needed. An efective robust scheme
is similar to that described by Grundy et al. 1998 which calculates contributions ater
minimising the group coancestry among all parents weighted by use not only the set of proposed matings and utilising maximum avoidance of relatives in matings i.e. α 0.
Here the group coancestry is ½c
T
Ac where c is the vector of contributions to the next
generation and A is the numerator relationship matrix. In a comparison Fernandez et al.
2003 suggest that such designs are more robust than Sanchez et al. 2003: however
this paper ignores the principles that underpin the latter method In particular, Sanchez et al. 2003 show a ‘best’ scheme is not necessarily based on avoidance of relatives in
mating and it is reasonable to expect continuity in the underlying theory as a function of the variance of the ‘noise’ in producing the required ofspring. While this research
question is being resolved the minimisation of group coancestry is recommended and described in chapter 8.
here are some commonly done things that should not be done since they fail to avoid
the development of unnecessary genetic bottlenecks and the consequent waste of genetic variation: 1 managing diversity by inbreeding coeicients of the parents;
2 managing diversity by the inbreeding coeicient of the ofspring; 3 using what is known as the ‘efective number of founders’ since this only manages contributions
in an arbitrary ‘founding’ generation and, as schemes develop, contributions from all generations need to be managed, not only founders.
Equation 7.1 also gives indications on aspects of management and the culture of management that will contribute to or hamper good genetic management. here
are a number of factors that will increase ΔF as a result of introducing variation in contributions. Examples of these are:
154 Utilisation and conservation of farm animal genetic resources
John Woolliams
1. Unequal mating opportunity e.g. when one sire is allocated many mates but another is allocated very few, perhaps through the unregulated use of AI for some sires, or
when one sire is kept over many breeding seasons but another is culled early in its breeding life.
2. If ofspring have diferential survival due to diferential management of families, or inherited disease or perceived ‘faults’. he latter problem comes from the imposition
of breed standards, usually based on exterior appearance, where ofspring failing to meet standards are excluded from breeding opportunities. he dangers of this are
that there is a reluctance to breed from certain individuals because their ofspring have attained a bad reputation and this problem can be compounded by secrecy in
the results of these examinations. he impact upon the population is to unnecessarily erode the genetic base. A more progressive strategy for both inherited disease and
breed ‘faults’ is to use the test results to identify the degree to which the problem is genetic, and which individuals are more or less likely to carry such genes, and to
develop a breeding scheme to reduce the incidence of the disease or the ‘faults’ in a sustainable way. his is an application of optimum contributions as developed in
chapter 8.
3. Artiicial selection will oten introduce variation in contributions, although selection within families will have no, or only small, impact. Selection may be desirable, e.g.
as mentioned above in 2, and is discussed in more detail later. Many problems are caused by fashion in favouring one sire over another e.g. according to performance
in particular shows in which the animal was judged as ‘best’, and this can result in big demands for matings to these sires, with consequently very unequal contributions.
his is a diicult social problem for many breeds, since their genetic management is shared amongst many private individuals as a hobby. However it is feasible to
develop rules or quotas that retain rewards for owners of individual animals, whilst managing the impact of such activities on the long-term diversity, and these should
be pursued wherever possible. More systematic genetic selection is considered in a later section and its implementation in chapter 8.
3.3. Impact of genomics
Is managing the pedigree the entire answer? In many cases yes, however Wang and Hill 2000 pointed out that efective population sizes could in theory be made ininite if
selection was made actively based upon the alleles that were inherited by the ofspring. his could further reduce the loss of diversity by ensuring that the replacement parents
contain a balanced number of copies of each segment of DNA from each parent, although equality among segments will remain impossible if the mating ratio, d 1. If d
=1 than this would result in no loss of diversity and an ininite efective population size. his ideal is unachievable in practical terms requiring very large families for a genome
